The hydro-aerodynamic theory of sailing shows that optimizing sailboat performance is extremely complicated. There are also many complex inter-relationships between the many factors affecting sailboat performance. If we want to maximize boat speed (or other factor such as safety) External Factors such as wind speed, wind direction, variations in wind speed, variations in wind direction, and wave conditions will determine Optimum Setpoint Targets such as sail plan (size and type of sails used), sail shape, sail pressure distribution, boat heel, and rudder angle. In order to achieve these Optimum Setpoint Targets, various Control Variables such as forestay sag, mast bend, sheet tension, and halyard tension must be used. However, there is a complex inter-relationship between the Control Variables. For example both backstay tension and sheet tension will affect forestay sag which will affect the sail shape. Changes in mast bend will affect both jib and main sail shape.
In addition to the complex relationship between all of these variables, very small changes in a single variable may have an enormous effect on sailboat performance. For example, FIG. 2 (taken from page 329, Aero-Hydrodynamics of Sails by Marchaj) shows the effect of sail draft depth (or camber) on sail pressure, holding all other variables constant under carefully controlled laboratory conditions. As can be seen, an increase in draft depth from 16.3% to 18.6% causes an increase in maximum pressure coefficient from 1.6 to 2.0 (while also reducing negative pressure on the windward side). This seemingly insignificant change in draft depth, which cannot even be measured on board a racing sailboat, causes a 25% increase in sail pressure! Since sail pressure is the driving force that moves a boat through the water, it is obvious that precise measurement and control of the draft depth is critical to optimizing the boat's performance.
While such laboratory experiments demonstrate that precise measurements are critical to optimizing sailboat performance, the data cannot be used in isolation on an actual boat. Many other factors and relationships must also be considered.
For simplicity in illustration, we may isolate the effect of wind speed on optimum sail shape. Small variations in wind speed have a large effect on optimum sail shape (e.g. draft depth and location . . . ) for a given sail. Furthermore, small variations in sail shape have a large effect on sail pressure and thus boat speed. These small and subtle changes are extremely difficult for the sailor to measure much less optimize.
For example, in a 4 knot wind the optimum draft depth for a given sail may be 10% and the optimum draft position may be 48%. In 8 knots the optimum may be 16% and 46%. In 12 knots the optimum may be 14% and 44%. In 18 knots the optimum may be 10% and 44%. However, in practice, it may be impossible for a sailor to measure by eye such subtle differences in draft depth and position even though such differences significantly affect boat speed. Furthermore; since wind direction, boat heel, rudder position, and other factors are constantly changing, it may be impossible for the sailor to even determine what the optimum sail shape should be, much less to measure what it is.
Some complexity may be added to this simple illustration. The optimum draft depth and position will vary from the foot to the head of both the jib and main sails, thus the sail twist must also be optimized. Also, rather than optimizing boat speed, we may optimize the "Velocity Made Good--Vmg" also known as Way Made Good (going fast toward the intended destination rather than just going fast). Finally, rather than looking at optimizing sail shape, we can look at the effect of changing one Control Variable, the sheeting angle.
FIG. 3 (from page 28, Aero-Hydrodynamics of Sails by Marchaj) shows the effect of sheeting angle (.delta.m), wind speed (V.sub.A), and course heading (.beta.) on Velocity Made Good (Vmg) under carefully controlled conditions in a wind tunnel. This shows that a wind speed increase from 10 to 14 knots requires a significant change in both boat heading and sheeting angle to maximize Velocity Made Good. At 10 knots (the second line from the left), the maximum is achieved at a heading of 25.degree. and sheeting angle of 5.degree.. At 14 knots (the third line from the left), the maximum requires a change to a heading of 29.degree. and a sheeting angle of 14.degree.. Failure to make the proper course and sheeting adjustments will result in a decrease in maximum velocity made good of over 10%. While such a minor adjustment is extremely difficult to detect, this could easily cost the race. A 12 minute difference over a 2 hour race is often the difference between first and last place!
This simple illustration shows two critical aspects addressed by the present invention. First of all, it is important, but difficult, to determine what the Optimum Target Setpoints should be. Secondly, it is important, but difficult, to measure small variations in Setpoints and Control Variables (e.g. sail shape and sheeting angle) that significantly affect the boat's performance. The present invention addresses both of these needs, providing accurate data and a means for determining and reproducing optimum sailing conditions.
There is relatively little prior art related to implementing a system that meets both these needs. On the one hand, there are prior inventions that fail to account for anywhere near the complexity of an actual racing sailboat. These prior inventions essentially tie a single sensor (such as wind direction or wind speed through the slot) to a single control variable (such as rudder angle or sail angle). Many of these prior inventions are mechanical attachments that automatically adjust for changes in wind direction in order to keep the boat headed in the right direction or keep the sails somewhat properly adjusted. None adequately account for the huge scale of complexity that is addressed by the present invention. In fact, very few of these types of prior inventions have found commercial use due to their very limited usefulness.
On the other hand, there is a limited body of literature that specifically addresses the aero-hydrodynamic theory of sailing. In these texts, cumbersome experiments are performed using wind tunnels and large sensors that are impractical for use in actual sailboat racing. For example, as recently as 1994 Lombardi and Tonelli published an experimental determination of the pressure distribution on a sail. They used liquid manometers connected by 1.5 mm diameter tubes to probes hung onto the sails. The fluctuations in liquid levels in these manometers were videotaped and then later replayed and manually transcribed to obtain the data desired. Obviously such a cumbersome system could never be used on a racing sailboat.
Another limitation with much of the present body of scientific literature is that the sailor cannot directly measure the data used by the theory. An example is shown in FIGS. 4 and 5. These figures show the desire to plot Apparent course (.beta.) or true course (.gamma.) versus velocity made good (Vmg). However, the sailor cannot directly measure Vmg nor .gamma. nor .beta.; he can only measure the boat speed V.sub.S and apparent wind direction (.beta.-.lambda.). Another limitation is that the theories assume that the true wind direction is always constant and that the sailor's desired Vmg is always parallel to the true wind direction. This is normally correct at the start of the race which is always a beat into the wind. However, once the wind shifts (and it always does) or the sailor is no longer directly downwind from the mark, the desired maximization of Vmg changes from the traditional relationships (it is no longer simply V.sub.S.times.cos .gamma.). Looking at the polar diagram in FIG. 5, a sailor wanting to maximize Vmg in 7 knot winds would always steer a .gamma. of 47.degree. (it is difficult from this plot to determine what .beta. or .beta.-.lambda. course to actually steer--recall that the helmsman cannot measure .gamma.). However, if the wind shifts 20.degree. counterclockwise, the entire polar plot would also rotate 20.degree. and the new max Vmg would be at a .gamma. of greater than 47.degree..
As can be seen, the theory provides many good clues for optimizing sailing performance, but actually implementing the theory is cumbersome if not impossible. Taking the appropriate data and making the calculations and many corrections is extremely difficult and an on-board computerized system as in the present invention is required to properly implement the theory.
Virtually all sailors will have existing commercial sensors that provide wind speed, wind direction, boat speed, boat direction and backstay tension. Sophisticated sailors can also use their global positioning system (GPS) to determine average Vmg. Some may even measure rudder position through their commercial auto pilot device. However, these existing systems fail to measure a wide range of critical pieces of information such as sail shape, sail twist, sail pressure distribution, mast bend, forestay sag, and boat heel. Also, there is no existing system for presenting sensor information or relationships in a useful graphical format for performance optimization. Instead, the sailing literature provides a great many useful tips, rules-of-thumb, and rudimentary notes such as the Trim Card Samples by Whidden and Levitt shown in FIG. 6.
Although various advanced sensors have been applied to aircraft wings, medical devices, and electronics manufacturing, these technologies have not in general been implemented for use on sailboats or recreational boating applications. Application of such sensors requires significant adaptations to implement them on a sailboat or recreational boating application.
Although aero-hydrodynamic theory teaches that certain relationships between factors are extremely important (e.g. boat speed vs. heading or sail shape), there are no known systems available for gathering and displaying such information to the sailor in a useful format.
Take for example, the simple desire to plot maximum boat speed vs. heading for a given wind speed and sail shape. While trying to take this data from existing sensors' analog indicators, the wind speed will vary and shift and the helmsman will vary rudder angle and heading. Thus obtaining even this simple plot is extremely difficult. Add to this the many other factors affecting boat speed and it is readily apparent that this is a time consuming and inaccurate method for obtaining this vital relationship. The racing sailor may need dozens of such relationships, plotting boat speed or velocity made good versus different sail plans, sail shapes, etc. for different wave conditions and wind speeds. Without the present invention, obtaining such relationships could take hundreds of hours and still be somewhat inaccurate.
The benefits of this invention to the racing sailor are thus readily apparent. The system will provide not only accurate measurements, but can also be used to pick out the most important data from a complex jumble of data points to plot critical relationships. The system can calculate and display, for example, the following information:
Plot Vmg versus boat heading, sail shape, sail plan, sheeting angle . . . for different wind speeds and different sea states. PA1 Revise Vmg optimization plans as the direction to the mark changes or the wind changes (e.g. rotate the polar diagram and revise all recommended target control settings). PA1 Wind speed and direction as a function of time (thus the sailor will be able to anticipate future wind shifts). PA1 Rudder position as a function of time (showing how steady the helmsman is). PA1 Time required to tack or gibe and regain prior boat speed (showing how fast the crew is at tacking or gibing). PA1 Fluctuation in tacking time (showing how consistent the crew is or whether they improve during the course of a racing season). PA1 Time required to make a sail change (showing crew performance and consistency). PA1 Graphically show the boat heading, wind direction, leeway, and rudder position (shows whether the boat is properly balanced). PA1 Plot forestay sag and mast bend versus backstay tension at different wind speeds. PA1 Show sail stress to determine when the sail must be changed or reefed for safety reasons. Also the sail stretch over time may be shown. PA1 Show current boat speed under current conditions benchmarked against best prior boat performance.
Today, sailors must use trial and error and benchmark their performance against other boats. Thus learning to improve performance may take many years of experience in different conditions against different boats to discover what works best. In fact, many sailors never do learn why they fail to achieve top performance and remain at the back of the fleet forever.
The present invention can be used to benchmark the boat against itself. This performance benchmarking does not require racing against other boats. This dramatically improves the ability to determine optimum settings since the sailing team can concentrate on improving sail trim and boat performance on their own rather than worrying about wind shifts, running into other boats, rounding marks or the many other distractions during a race.
In addition to being of value to the racing sailor, the present invention is of value to the recreational boater as well. Instead of optimizing boat speed, the system can be used to optimize passenger comfort, boat safety, or other desires. Also, if the boat is properly equipped with automatic winches and other hardware, the system can be used for feedback control so that the boat can be piloted automatically or remotely.
The present invention thus provides unique and useful benefits to sailors. The system can take existing sensor information and present it in a more useful format showing important relationships and/or graphical format. New sensors can also be added to the system to measure critical parameters and further improve sailboat performance. Since the system is modular, a simple base system can be installed on a boat and new sensors and software upgrades can be added over time.